Forging new generations of engineers

Geometric Shapes and Area

Shape Shape describes the two-dimensional contour that characterizes an object or area, in contrast to a three-dimensional solid. Examples include:

Area Area is the extent or measurement of a surface. All shapes represent enclosed two-dimensional spaces, and thus have area.

Circles A circle is a round plane figure whose boundary consists of points equidistant from the center.

Circles The circle is the simplest and strongest of all the shapes. Circles are found within the geometry of countless engineered products, such as buttons, tubes, wires, cups, and pins. A drilled hole is also based on the simple circle.

Area of a Circle In order to calculate the area of a circle, the concept of  (pi) must be understood.  is a constant ratio that exists between the circumference of a circle and its diameter. The ratio states that for every unit of diameter distance, the circumference (distance around the circle) will be approximately 3.14 units.

Area of a Circle To calculate the area of a circle, the radius must be known.  = 3.14 r = radius A = area A =  r 2

Ellipses An ellipse is generated by a point moving in a plane so that the sum of its distances from two other points (the foci) is constant and equal to the major axis.

Ellipses To calculate the area of an ellipse, the lengths of the major and minor axis must be known. a = major axis b = minor axis  = 3.14 A = area A =  (.5a)(.5b)

Polygons A polygon is any plane figure bounded by straight lines. Examples include the triangle, rhombus, and trapezoid.

Geometric Shapes and Area Introduction to Engineering Design TM Unit 2 – Lesson 2.1 – Geometric Shapes and Solids Triangles A triangle is a three-sided polygon. The sum of angles of a triangle will always equal 180°. There are three types of triangles: Right triangle Acute triangle Obtuse triangle Project Lead The Way, Inc. Copyright 2007

Geometric Shapes and Area Introduction to Engineering Design TM Unit 2 – Lesson 2.1 – Geometric Shapes and Solids Triangles Sign support truss based on a right triangle. Light weight space frame roof system based on the equilateral triangle The triangle is the simplest, and most structurally stable of all polygons. This is why triangles are found in all types of structural designs. Trusses are one such example. Project Lead The Way, Inc. Copyright 2007

Geometric Shapes and Area Introduction to Engineering Design TM Unit 2 – Lesson 2.1 – Geometric Shapes and Solids Triangles Sometimes the terms inscribed and circumscribed are associated with the creation of triangles and other polygons, as well as area calculations. Project Lead The Way, Inc. Copyright 2007

Geometric Shapes and Area Introduction to Engineering Design TM Unit 2 – Lesson 2.1 – Geometric Shapes and Solids Area of a Triangle To calculate the area of any triangle, the base and height must be known. b = base h = height A = area A = .5(bh) Project Lead The Way, Inc. Copyright 2007

Geometric Shapes and Area Introduction to Engineering Design TM Unit 2 – Lesson 2.1 – Geometric Shapes and Solids Quadrilaterals A quadrilateral is a four-sided polygon. Examples include the square, rhombus, trapezoid, and trapezium: Project Lead The Way, Inc. Copyright 2007

Geometric Shapes and Area Introduction to Engineering Design TM Unit 2 – Lesson 2.1 – Geometric Shapes and Solids Parallelograms A parallelogram is a four-sided polygon with opposite sides parallel. Examples include the square, rectangle, rhombus and rhomboid Project Lead The Way, Inc. Copyright 2007

Geometric Shapes and Area Introduction to Engineering Design TM Unit 2 – Lesson 2.1 – Geometric Shapes and Solids Parallelograms To calculate the area of a parallelogram, the base and height must be known. b = base h = height A = area A = bh Project Lead The Way, Inc. Copyright 2007

Geometric Shapes and Area Introduction to Engineering Design TM Unit 2 – Lesson 2.1 – Geometric Shapes and Solids Regular Multisided Polygons A regular multisided polygon has equal angles, equal sides, and can be inscribed in or circumscribed around a circle. Examples of regular multisided polygons include the pentagon, hexagon, heptagon, and octagon. Project Lead The Way, Inc. Copyright 2007

Geometric Shapes and Area Introduction to Engineering Design TM Unit 2 – Lesson 2.1 – Geometric Shapes and Solids Multisided Polygons To calculate the area of a multisided polygon, a side length, distance between flats (or diameter of inscribed circle), and the number of sides must be known. Project Lead The Way, Inc. Copyright 2007

Geometric Shapes and Area Introduction to Engineering Design TM Unit 2 – Lesson 2.1 – Geometric Shapes and Solids Multisided Polygons Area calculation of a multisided polygon: s = side length f = distance between flats or diameter of inscribed circle n = number of sides A = area A = n s(.5f) 2 Project Lead The Way, Inc. Copyright 2007